Tomographic 3d imaging with a camera array

ABSTRACT

A tomographic 3D imaging system includes a conic-section mirror serving as the imaging objective, a sample holder positioned to hold a sample at a focus (fp) of the conic-section mirror, a light source directing light to the sample, and an array of camera sensors positioned above the conic-section mirror. In some cases, the array of camera sensors is positioned parallel to a directrix of the conic-section mirror. In some cases, the conic-section mirror is a parabolic mirror. In some cases, each camera sensor of the array of camera sensors is positioned facing the sample holder at an inclination angle dictated by a lateral position of the camera sensor according to θ(r)=2 tan−1(r/2fp), where r is the radial entry position across the parabolic mirror.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application Ser.No. 63/310,725, filed Feb. 16, 2022.

BACKGROUND

Non-invasive tomographic three-dimensional (3D) imaging hasrevolutionized basic scientific and medical research by revealinginternal structures in their native biological context within thicksamples. However, dense tomographic 3D imaging requires potentiallyorders of magnitude more data than two-dimensional (2D) imaging, makinghigh-speed tomographic imaging very challenging. For example,point-scanning techniques, such as confocal microscopy and multiphotonmicroscopy can be slow due to the need to perform inertially-constrainedscanning of a focused point in three dimensions. Computationalreconstruction techniques such as those used in optical projectiontomography and optical diffraction tomography (ODT) can require hundredsof multi-angle images.

When attempting to speed up the scanning or reconstruction, techniquesthat perform data under-sampling and that use compressive sensingtechniques to fill in the information gaps, while useful in a fewapplications, often rely heavily on regularization or priors, such as atotal variation (TV) or spatial sparsity, whose assumptions are notalways met. Thus, the large data requirement for dense tomographicimaging often necessitates chemically fixing, immobilizing, or otherwiserestricting the sample's movements, thereby disrupting its naturalphysiological state. Therefore, there is a need for tomographic imagingtechniques that allow for tomographic imaging of unrestrained organisms.

BRIEF SUMMARY

The systems and methods described herein enable tomographic 3D imagingusing an array of cameras. The described 2π Fourier light fieldtomography (2π-FLIFT) imaging system allows for synchronized snapshotsof a sample taken from multiple views over a wide angular range withoutperturbing the sample, from which a dense 3D volume can becomputationally reconstructed. The described systems and methods may beapplied to image freely-moving model organisms or can provide surgicalguidance at millimeter-to centimeter-scale fields of view and at highspeeds.

A tomographic 3D imaging system includes a conic-section mirror servingas the imaging objective, a sample holder positioned to hold a sample ata focus (f_(p)) of the conic-section mirror, a light source directinglight to the sample, and an array of camera sensors positioned above theconic-section mirror.

This Summary is provided to introduce a selection of concepts in asimplified form that are further described below in the DetailedDescription. This Summary is not intended to identify key features oressential features of the claimed subject matter, nor is it intended tobe used to limit the scope of the claimed subject matter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a 2π Fourier light field tomography imaging system.

FIG. 2 illustrates an example configuration of an array of camerasensors for use in a 2π-FLIFT imaging system.

FIG. 3A illustrates a 2π-FLIFT imaging system with an array ofapertures.

FIG. 3B illustrates an example array of apertures.

FIG. 4 illustrates an example 2π-FLIFT imaging system calibrationmethod.

FIG. 5 illustrates a specific embodiment of dynamic tomographicreconstruction of a 3D object.

FIG. 6A illustrates a system controller for implementing functionalityof a 2π-FLIFT imaging system.

FIG. 6B illustrates a computing system that can be used for a 2π-FLIFTimaging system.

DETAILED DESCRIPTION

The systems and methods described herein enable tomographic 3D imagingusing an array of cameras. The described 2π Fourier light fieldtomography (2π-FLIFT) imaging system allows for synchronized snapshotsof a sample taken from multiple views over a wide angular range. withoutperturbing the sample, from which a dense 3D volume can becomputationally reconstructed. The described systems and methods may beapplied to image freely-moving model organisms or can provide surgicalguidance at millimeter-to centimeter-scale fields of view and at highspeeds.

FIG. 1 illustrates a 2π Fourier light field tomography imaging system.Referring to FIG. 1 , the 2π-FLIFT imaging system 102 includes aconic-section mirror 104, a light source 106, a sample holder 108, andan array of camera sensors 110.

The array of camera sensors 110 includes a plurality of camera sensors(e.g., camera sensor 114). The 2π-FLIFT imaging system 102 may furtherinclude an array of lenses 112. The array of lenses 112 includes aplurality of lenses (e.g., lens 116), each lens 116 corresponding to acamera sensor 114 of the array of camera sensors 110. Each lens 116 inthe array of lenses 112 is positioned a focal length distance (f_(lens))away from the corresponding camera sensor 114 in the array of camerasensors 110 so that the object planes are at infinity. Central chiefrays 120 (or optical axes) pass through the lenses of the array oflenses 112 for each camera sensor 114/lens 116 pair.

In some cases, the conic-section mirror 104 is a circular paraboloid(e.g., a parabolic mirror). In some cases, the conic-section mirror 104has exactly one axis of symmetry (i.e., the parabolic axis 122). In somecases, on the parabolic axis 122 of the conic-section mirror 104, thereis a focus (or focus point). In some cases, the focus (f_(p)) is a fixedpoint located inside the conic-section mirror 104 and is the point towhich all on-axis rays (parallel to the parabolic axis 122 of theconic-section mirror 104) converge. In some cases, the directrix 124 ofthe conic-section mirror 104 is a straight line in front of theconic-section mirror 104 and is perpendicular to the parabolic axis 122.

The sample holder 108 is positioned to hold the sample 118 at the focus(f_(p)) of the conic-section mirror 104. The sample holder 108 istransparent to maximize visibility of the sample 118 within the sampleholder 108. In some cases, the sample holder 108 has a uniform wallthickness. Examples of preferred shapes for the sample holder 108include a spherical shell or a cylindrical tube. For example, nuclearmagnetic resonance (NMR) spectroscopy tubes (which are transparent,round-bottomed, and are produced to have as uniform wall thickness aspossible) may be used as a sample holder. The sample holder 108 size maybe dependent on the imaging problem scale.

The sample 118 is illuminated by a light source (e.g., light source106). In some cases, as illustrated in FIG. 1 , the sample 118 isilluminated though an aperture 126 at the bottom of the conic-sectionmirror 104. The aperture 126 is sized so that it is large enough toallow adequate illumination light to pass through, but small enough toavoid preventing signal from reaching the center-most camera sensor 114of the array of camera sensors 110. In some cases, the sample 118 isilluminated by a light source which directs light from above (notshown).

The conic-section mirror 104 is sized relative to the array of camerasensors 110, such that the conic-section mirror 104 can act as a commonreflective object for each camera sensor 114 in the array of camerasensors 110. The array of camera sensors 110 is positioned with eachcamera sensor 114 of the array of camera sensors 110 facing the sampleholder 108. The array of camera sensors 110 and the array of lenses 112are parallel to the directrix of the conic-section mirror 104 (i.e.,perpendicular to the parabolic axis of the conic-section mirror 104).

To obtain multi-view images of the sample 118, each camera sensor 114captures one or more images of the sample 118 from a differentinclination angle. In cases in which the conic-section mirror 104 is aparabolic mirror, the inclination angle of each camera sensor 114 isdictated by a lateral position of the camera sensor 114 according to thefollowing equation:

${{\theta(r)} = {2{\tan^{- 1}\left( \frac{r}{2f_{p}} \right)}}},$

where r is the radial entry position across the conic-section mirror104. Although this equation is specific to parabolic mirrors, thisequation (and others described herein) can be modified (e.g., via knownmodifications that are apparent to those having ordinary skill in theart) to account for other types of conic-section mirrors, including butnot limited to spherical and ellipsoidal mirrors.

Therefore, as long as the lateral position of the outermost camerasensor (outermost relative to the parabolic axis 122 of theconic-section mirror 104) is equal to or greater than 2f_(p) from theparabolic axis 122 of the conic-section mirror 104, the array of camerasensors 110 of the 2π-FLIFT imaging system 102 can obtain multi-viewimages over at least 2π steradians. In some cases, the outermost camerasensor of the array of camera sensors 110 from the parabolic axis 122 ofthe conic-section mirror 104 is less than 2f_(p). In some cases, theoutermost camera sensor of the array of camera sensors 110 from theparabolic axis 122 of the conic-section mirror 104 is equal to 2f_(p).In some cases, the outermost camera sensor of the array of camerasensors 110 from the parabolic axis 122 of the conic-section mirror 104is greater than 2f_(p).

In some cases, the 2π-FLIFT imaging system 102 further includes a systemcontroller (e.g., controller 604 of FIG. 6A). In some cases, the systemcontroller is coupled to the array of camera sensors 110 to receive data(e.g., the images) from the camera sensors 114. In some cases, aconic-section mirror 104 can be a parabolic reflector.

FIG. 2 illustrates an example configuration of an array of camerasensors for use in a 2π-FLIFT imaging system (e.g., 2π-FLIFT imagingsystem 102). The array of camera sensors 200 is an array of individualcamera sensors 202 arranged in an X-Y plane (e.g., an X-Yconfiguration). For example, the array of camera sensors 200 depictedFIG. 2 (as well as array of camera sensors 114) are arranged in a 6camera sensor by 9 camera sensor configuration, for a total of 54individual camera sensors 202. The individual camera sensors 202 of thearray of camera sensors 200 are equally spaced with respect to oneanother, having an inter-camera spacing of (p). For example, in somecases, the individual camera sensors 202 have an inter-camera spacing ofp=13.5 mm. In some cases, the inter-camera spacing is any width that islower-bound limited by the camera sensor width (e.g., so that the camerasensors do not overlap) and would not include an upper-bound limit solong as the conic-section and/or parabolic mirror is an adequate size.While not shown in FIG. 2 , the array of lenses (e.g., array of lenses112 of FIG. 1 ) would be similarly configured such that the lenses inthe array of lenses would align with the individual camera sensors 202in the array of camera sensors 200.

In some cases, the field of view (FOV) of tomographic 3D reconstructionmay be limited by the depth of field of the conic-section and/orparabolic mirror and its tilt aberrations. One solution may involveusing lenses with different focal lengths in the array of lenses. Insome cases, this is accomplished by physically swapping out the lensesfor lenses with different focal lengths. In some cases, the array oflenses includes lenses with refocusable lens units. In some cases, toincrease spatial resolution to a tomogram, the 3D FOV can be sacrificedby increasing the aperture sizes in the array of apertures 316.

FIG. 3A illustrates a 2π-FLIFT imaging system with an array ofapertures. The 2π-FLIFT imaging system 302 includes a conic-sectionand/or parabolic mirror 304, a light source 306, a sample holder 308, anarray of camera sensors 310, an array of lenses 312, a fluorescenceemission filter array 314 and an array of apertures 316.

The fluorescence emission filter array 314 is positioned between thearray of camera sensors 310 and the sample holder 308. The fluorescenceemission filter array 314 can be inserted directly below the array oflenses 312.

The array of apertures 316 includes a plurality of apertures, eachaperture corresponding to a lens/camera sensor pair of the array oflenses 312 and the array of camera sensors 310. The array of apertures316 may be approximately (f_(lens)) below the principal plane of thearray of lenses 312 (e.g., their Fourier planes).

FIG. 3B illustrates an example array of apertures. Referring to FIG. 3B,the apertures (e.g., aperture 318 and aperture 320) of the array ofapertures 316 can have varying diameters. The variation in the diametersof the individual apertures of the array of apertures 316 tunes thelateral resolution and depth of field, and also accounts for incidentangle-dependent effective focal lengths. When using an array ofapertures, such as the array of apertures 316, the effective focallength increases according to the equation:

${f_{eff}(r)} = {f_{p} + \frac{r^{9}}{4f_{p}}}$

in the case of a parabolic mirror. Although this equation is specific toparabolic mirrors, this equation (and others described herein) can bemodified (e.g., via known modifications that are apparent to thosehaving ordinary skill in the art) to account for other types ofconic-section mirrors, including but not limited to spherical andellipsoidal mirrors.

A diameter of each aperture of the array of apertures 316 may increasein diameter from a center of the array of camera sensors to a peripheryof the array of camera sensors (e.g., compared to a center of the arrayof camera sensors). For example, the diameter of aperture 318 is largerthan the diameter of aperture 320.

Computational Modeling of the Imaging Optics

In order to perform 3D reconstructions of images taken by a 2π-FLIFTimaging system, it is beneficial to model the ray trajectoriespropagating between camera sensors and the sample. Bundle adjustment(BA) is simultaneous refining of the 3D coordinates describing the scenegeometry, the parameters of relative motion, and the opticalcharacteristics of the camera sensors used to acquire the images, givena set of images depicting a number of 3D points from various viewpoints. Rays can be propagated from the camera sensor to the sample orfrom the sample to the camera sensor. Traditionally, for BA algorithmsused in feature-point-based 3D point cloud reconstruction algorithms ina computer vision (e.g., photogrammetry and/or structure-from-motion),the rays are propagated from the sample to the cameras as part of aprocess called reprojection.

Because a parabolic mirror used in the 2π-FLIFT imaging system isunlikely to be perfectly parabolic (e.g., due to manufacturing errors)and since optics of the sample holder may be difficult to modelparametrically, the ray propagation results can be refined withnonparametric modeling (e.g., polynomials, Zernike polynomials, kernelestimation).

To calibrate misalignments and imperfections of the 2π-FLIFT imagingsystem, a calibration can be carried out on the camera array and mirrorusing, for example a fiber optic cannula with a diffuser tip mounted ona 3-axis motorized translation stage. In some cases, the 2π-FLIFTimaging system may include a single fluorescent microsphere (as opposedto the fiber optic cannula). Other calibration methods can be used,including for the sample holder (e.g., a NMR tube) and for thereconstruction methods (e.g., refining sample-incident rays andestimation of a low resolution reconstruction).

FIG. 4 illustrates an example 2π-FLIFT imaging system calibrationmethod. The calibration method 400 includes scanning (402) a fiber opticcannula diffuser tip at a plurality of scan positions of apre-programmed 3D pattern at a 3D field of view of the tomographyimaging system, capturing (404) images of the fiber optic cannuladiffuser tip with each camera sensor of the array of camera sensors ateach of the plurality of scan positions of the pre-programmed 3Dpattern, segmenting and localizing (406) the captured images of thefiber optic cannula diffuser tip, calibrating (408) the tomographyimaging system using a bundle adjustment algorithm, and modelling (410)refraction through the sample holder of the tomography imaging systemimaging system. The tomography imaging system may further include acontroller (e.g., controller 604 of FIG. 6A), which is configured toperform the calibration method 400.

In some cases, scanning (402) the fiber optic cannula includes movingthe cannula fiber in a pre-programmed (i.e., “known”) 3D pattern acrossthe 3D FOV of the 2π-FLIFT imaging system. An example 3D pattern is a 3Dgrid. While the fiber optic cannula is scanned (402) in thepre-programmed 3D pattern, the camera sensors in the array of camerasensors of the 2π-FLIFT imaging system capture (404) images of the fiberoptic cannula at a plurality of scan positions. In the images capturedby the camera sensor, the fiber optic cannula's diffuser tip will showup as a single small point in each image. The captured images aresegmented and localized (406) as feature points in the BA algorithm tocalibrate system misalignments and imperfections.

The 2π-FLIFT imaging system may then be calibrated (408) using amodified BA algorithm. The disclosed BA algorithm propagates the raysfrom the camera sensors to the sample (as opposed to traditional BAalgorithms which propagate the rays from the sample to the sensor).Therefore, the disclosed BA algorithm (e.g., backwards BA algorithm)computes a back-projection error in a sample rather than thereprojection error in the camera space.

The back-projection error is computed by minimizing the shortestdistance between each ray and the object point to which it corresponds.That is, given a ray defined by r=(z, y, z)^(T), a unit vector u=(u_(x),u_(y), u_(z))^(T), and an object point r_(obj)=(x_(obj), y_(obj),z_(obj))^(T) (all defined as column vectors), the shortest distance isgiven by d_(min)=|r_(closest)−r_(obj)|, wherer_(closest)=r+((r_(obj)−r)·u)u is the closest approach of the ray to theobject point. The object point is the localized images of the fiberoptic cannula. This minimizes the mean square distance of every ray toits corresponding object point with respect to the optical systemcalibration parameters. In addition to optimizing the optical systemparameters, the disclosed method can also optimize the relative 6D poseof the stage trajectory.

The bundle algorithm providing the “best” point of intersection, given acollection of rays indexed by i, {r_(i), u_(i)}_(i), can be shown to be:

${{\overset{\hat{}}{r}}_{obj} = {{\arg\min{\sum\limits_{i}{❘{r_{{closest},i} - r_{obj}}❘}}} = {\left\lbrack {\sum\limits_{i}\left( {{u_{i}u_{i}^{T}} - I_{3}} \right)} \right\rbrack^{- 1}\left\lbrack {\sum\limits_{i}{u_{i}u_{i}^{T}r_{i}}} \right\rbrack}}},$

where I₃ is a 3×3 identify matrix.

This approach is advantageous over a random distribution of pointemitters. First, because the fiber tip is in the air, there is no needto model the sample holder's optics at the same time, thus simplifyingthe calibration problem. Second, this method does not require matchingpoints across different images, which may be thwarted by similarity inappearance of different point emitters within the sample. Thus, sincethe trajectory of the fiber tip is pre-programmed, the ground truthlocation is known.

However, there may be cases where the object points are unknown. In thiscase, the object points can be treated as optimizable variables orcomputed as the points that minimize the closest distance squared to allrays that correspond to the same object point.

Modelling (410) the refraction through the sample holder can beaccomplished using Snell's law and modelling the sample holder as acylindrical tube with a hemispherical tip with a radius r and a uniformwall thickness t. If the material is known, the refraction index (RI)can be fixed, or the RI of the wall, as well as the RI of the medium inwhich the sample resides (e.g., water or air), may be fine tuned.Alternatively, or in addition, the refraction can be modelednonparametrically (e.g., polynomial coefficients with no physicalmeaning).

For a calibration sample, the step of scanning the fiber cannula may beemployed after placing the fiber cannula within the sample holder (iffeasible). In some cases, a random distribution of fluorescentmicrospheres may yield an easier reconstruction given the alreadyoptimized system calibration parameters for everything but the sampleholder. This step may also be combined with a tomographic samplereconstruction algorithm.

Tomographic Reconstruction

After the 2π-FLIFT imaging system parameters are calibrated (e.g., viamethod 400 described with respect to FIG. 4 ) the rays from the sensorto the conic-section and/or parabolic mirror's focus (i.e., where thesample is positioned) may be accurately propagated. There are severaloptions for the sample tomographic reconstruction algorithm. Theseoptions depend on the assumptions made with respect to the light-sampleinteraction. In some cases, the simplest reconstruction algorithm may beone similar to the ray-based filtered back-projection algorithm used incomputed tomography (CT). In some cases, a modified version of thealgebraic reconstruction technique (AR) may be used. In some cases,wave-based models may also, or alternatively be used.

In some cases, a gradient-based algorithm that iteratively minimizeserror between a forward prediction based on a physical light propagationmodel and the measured camera data (e.g., captured images) is utilizedthat updates the 3D or 4D (e.g., 3D plus time, such as a 3D video feed)reconstruction of the moving object. For example, for a 3D tomographicreconstruction image, the 2π-FLIFT imaging system can include acontroller (e.g., controller 604 of FIG. 6A) having a processor and amemory storing instructions that direct the imaging system tosimultaneously capture a set of images of the sample and create (e.g.,computationally) a 3D tomographic reconstruction image from set ofimages. Each camera sensor of the array of camera sensors captures animage of the set of images. As another example for 4D tomographicreconstruction images/video feed, the instructions can direct theimaging system to capture a plurality of sets of images of the sampleand create (e.g., computationally) a plurality of 3D tomographicreconstruction images from the plurality of sets of images. In thisexample, each set of images of the plurality of sets of images arecaptured simultaneously, each camera sensor of the array of camerasensors captures one image for each set of images of the plurality ofsets of images, and an image of the plurality of 3D tomographicreconstruction images is created for each set of images of the pluralityof sets of images.

One example approach may be used with the 2π-FLIFT imaging system 302 ofFIG. 3A, which includes a fluorescence emission filter array (e.g.,fluorescence emission filter array 314). It is assumed that theillumination light evenly excites all fluorophores across aweakly-scattering 3D sample. Upon excitation, the fluorophores areassumed to emit fluorescence evenly in every direction, such that theincident illumination direction or angular distribution does not matter.A ray-based forward model involving projections along straight linesdefined by the result of ray propagation through the calibratedtomography imaging system can be used. The mean square error between thelinear projections and the measured data with respect to the sample 3Dreconstruction may be iteratively minimized. In some cases, when theexcitation light and fluorescence emission are significantly attenuatedby the sample due to scattering or absorption, the voxel-wise 3Dtomographic attenuation map is modeled. In some cases, sample-inducedrefraction is modeled to recover a voxel-wise tomographic RI map. Uponiterative reconstruction, the described methods can yield tomographic 3Dreconstructions of fluorescence, attenuation coefficients, and RI, amongother possibilities.

In some cases, when frame rates of the cameras are limited by datatransfer, the speed is improved by downsampling the images.Alternatively, or in addition to downsampling the images, to improvespeed, the images are cropped with a predefined crop, or asample-adaptive, content-aware cropping scheme.

FIG. 5 illustrates a specific embodiment of dynamic tomographicreconstruction of a 3D object. Referring to FIG. 5 , a single chief ray502 from one pixel 504 of one camera sensor 506 is illustrated forclarity, although it should be understood that chief rays from pixels ofevery camera sensor is used for dynamic tomographic reconstruction of a3D object 508. In the training step 510, n coordinates along the chiefrays are sampled and passed through the multilayer perceptron (MLP) 512to predict the fluorescence (F) and attenuation (μ) values at thosecorresponding coordinates. These values are used in the forward model topredict the measured intensity at the pixel, with the difference betweenthe measured intensity 514 and the prediction of the measured intensity516 being used to compute the mean square error (MSE) 518. The MSE 518is then minimized via stochastic gradient descent (SGD) 520 with respectto the MLP 512. After the training step 510, the inference step 522queries, by the MLP 512, the dense 4D coordinates 524 across all 3Dpositions across time to reconstruct the full, 2-channel dynamictomographic videos 526 with N frames.

Alternate Embodiments

In some cases, the tomography imaging system may not include aconic-section and/or parabolic mirror. In some cases, instead of aconic-section and/or parabolic mirror, the lenses in the array of lensesare positioned in a conic-section array (e.g., in the shape of aparabolic mirror). In some cases, the array of cameras spans the fullrotationally symmetric parabolic mirror.

In some cases, the array of cameras spans only half the parabolic mirrorwith a 90 degree-rotated sample. In this case, it could be easier toaccess the sample, as the sample would not be surrounded by almost allsides. In some cases, the array of cameras is in a circular arrangement(e.g., only along the boundary), wherein the radius of the circle is2f_(p). In some cases, the radius of the ring of cameras is less than2f_(p).

In some cases, the array of apertures includes arbitrary pupil patterns,specifying both amplitude and phase. In this case, the degree of freedomcould be useful in overcoming FOV limitations. In particular, thelimited depth of field of each camera image could be extended, forexample, using a cubic phase mask. Similarly, a pupil pattern could bedesigned to expand the lateral field of view of each camera in the arrayof cameras by overcoming the conic-section and/or parabolicmirror-induced tilt aberrations.

In some cases, the array of cameras, the array of lenses, and/or arrayof apertures laterally scans the sample and the conic-section and/orparabolic mirror in concert or, equivalently. Lateral scanning has theeffect of observing the sample from different incidence angles, allowingfor denser sampling of the 2π-steradian solid angle. In some cases, onlythe array of apertures is laterally scanned, which produces a similaraffect assuming the apertures are smaller than the lens apertures. Insome cases, the array of apertures is scanned axially, which changes theobject-side telecentricity and introduces a new angular information. Insome cases, the sample can be scanned in 3D to expand the 3D field ofview. In some cases, the array of lenses is axially scanned (e.g.,independently of the array of camera sensors).

Applications of the tomography imaging system can include imaging freelyswimming zebrafish larvae at high speed or imaging othermillimeter-scale model organisms. In addition, there are also potentialsurgical applications with certain configurations of the systems andmethods disclosed that may provide real-time 3D tomographic feedback notavailable in conventional microscope-guided surgeries. For example,existing surgical microscopes can be augmented by coaxially aligning theobject with a conic-section and/or parabolic mirror while having theimaging paths of the array of cameras and the array of lenses flankingthe surgical microscope so that they have entry positions beyond 2f_(p).

FIG. 6A illustrates a system controller for implementing functionalityof a 2π-FLIFT imaging system. Referring to FIG. 6A, a 2π-FLIFT imagingsystem 602 can include a controller 604 coupled to an array of camerasensors via a camera sensor interface 606 and a calibration interface608. In some cases, the controller 604 can include or be coupled to acommunications interface 610 for communicating with another computingsystem, for example computing system 612 of FIG. 6B. Controller 604 caninclude one or more processors with corresponding instructions forexecution and/or control logic for controlling the 2π-FLIFT imagingsystem (e.g., as described herein) and can include instructions(executed by the one or more processors) and/or control logic forcontrolling the calibration configuration as described with respect toFIG. 4 . Images captured by the camera sensors of the array of camerasensors can be processed at the controller 604 or communicated toanother computing device via the communications interface 610. In somecases, the controller 604 performs the method 400.

FIG. 6B illustrates a computing system that can be used for a 2π-FLIFTimaging system. Referring to FIG. 6B, a computing system 612 can includea processor 614, storage 616, a communications interfaces 618, and auser interface 620 coupled, for example, via a system bus 622. Processor614 can include one or more of any suitable processing devices(“processors”), such as a microprocessor, central processing unit (CPU),graphics processing unit (GPU), field programmable gate arrays (FPGAs),application-specific integrated circuits (ASICs), logic circuits, statemachines, application-specific standard products (ASSPs),system-on-a-chip systems (SOCs), complex programmable logic devices(CPLDs), etc. Storage 616 can include any suitable storage media thatcan store instructions 624 for generating composite images from themicro-camera array as well as the method 400. Suitable storage media forstorage 616 includes random access memory, read only memory, magneticdisks, optical disks, CDs, DVDs, flash memory, magnetic cassettes,magnetic tape, magnetic disk storage or other magnetic storage devices,or any other suitable storage media. As used herein “storage media” donot consist of transitory, propagating waves. Instead, “storage media”refers to non-transitory media.

Communications interface 618 can include wired or wireless interfacesfor communicating with a system controller such as described withrespect to FIG. 6A as well as interfaces for communicating with the“outside world” (e.g., external networks). User interface 620 caninclude a display on which the composite images can be displayed as wellas suitable input device interfaces for receiving user input (e.g.,mouse, keyboard, microphone).

Although the subject matter has been described in language specific tostructural features and/or acts, it is to be understood that the subjectmatter defined in the appended claims is not necessarily limited to thespecific features or acts described above. Rather, the specific featuresand acts described above are disclosed as examples of implementing theclaims and other equivalent features and acts are intended to be withinthe scope of the claims.

What is claimed is:
 1. A tomographic 3D imaging system, comprising: aconic-section mirror serving as the imaging objective; a sample holderpositioned to hold a sample at a focus (f_(p)) of the conic-sectionmirror; a light source directing light to the sample; and an array ofcamera sensors positioned above the conic-section mirror.
 2. The imagingsystem of claim 1, wherein the array of camera sensors is furtherpositioned parallel to a directrix of the conic-section mirror.
 3. Theimaging system of claim 1, wherein the conic-section mirror is aparabolic mirror.
 4. The imaging system of claim 3, wherein each camerasensor of the array of camera sensors is positioned facing the sampleholder at an inclination angle dictated by a lateral position of thecamera sensor according to${{\theta(r)} = {2\tan^{- 1}\left( \frac{r}{2f_{p}} \right)}},$ where ris the radial entry position across the parabolic mirror.
 5. The imagingsystem of claim 3, wherein an outermost camera sensor of the array ofcamera sensors from a parabolic axis of the parabolic mirror is lessthan 2f_(p).
 6. The imaging system of claim 3, wherein an outermostcamera sensor of the array of camera sensors from a parabolic axis ofthe parabolic mirror at 2f_(p).
 7. The imaging system of claim 3,wherein an outermost camera sensor of the array of camera sensors from aparabolic axis of the parabolic mirror greater than 2f_(p).
 8. Theimaging system of claim 1, wherein the conic-section mirror has anaperture at a bottom of the conic-section mirror and the light sourcedirects light to the sample through the opening of the conic-sectionmirror.
 9. The imaging system of claim 1, further comprising an array oflenses positioned between the array of camera sensors and the sampleholder, each lens of the array of lenses aligning with a correspondingcamera sensor in the array of camera sensors, wherein each lens of thearray of lenses is a focal length distance (f_(lens)) away from thecorresponding camera sensor of the array of camera sensors.
 10. Theimaging system of claim 9, further comprising a fluorescence emissionfilter array positioned between the array of lenses and the sampleholder and parallel to the array of lenses.
 11. The imaging system ofclaim 1, further comprising an array of apertures, each aperture of thearray of apertures aligning with a corresponding camera sensor in thearray of camera sensors, wherein a size of the array of correspondingapertures increases in diameter from a center of the array of camerasensors to a periphery of the array of camera sensors.
 12. The imagingsystem of claim 1, wherein the lenses are refocusable lens units. 13.The imaging system of claim 1, wherein the sample holder is atransparent container having a uniform wall thickness.
 14. The imagingsystem of claim 13, wherein the transparent container is a sphericalshell.
 15. The imaging system of claim 1, further comprising: a fiberoptic cannula with a diffuser tip; a 3-axis motorized translation stage,wherein the fiber optic cannula with the diffuser tip is mounted ontothe 3-axis motorized translation stage; and a controller comprising aprocessor and memory, the memory storing instructions that when executedby the controller, direct the imaging system to: scan the fiber opticcannula with the diffuser tip at a plurality of scan positions of apre-programmed 3D pattern at a 3D field of view of the imaging system;capture images of the fiber optic cannula with the diffuser tip witheach camera sensor of the array of camera sensors at each of theplurality of scan positions of the pre-programmed 3D pattern; segmentand localize the captured images of the fiber optic cannula diffusertip; calibrate the imaging system using a bundle adjustment algorithm;and model refraction through the sample holder of the imaging system.16. The imaging system of claim 10, wherein the bundle adjustmentalgorithm comprises a backwards bundle adjustment algorithm thatcomputes a back-projection error in the sample.
 17. The imaging systemof claim 1, further comprising a controller comprising a processor andmemory, the memory storing instructions that when executed by thecontroller, direct the imaging system to: simultaneously capture a setof images of the sample, wherein each camera sensor of the array ofcamera sensors captures an image of the set of images; and create a 3Dtomographic reconstruction image from set of images.
 18. The imagingsystem of claim 1, wherein the instructions further direct the imagingsystem to: capture a plurality of sets of images of the sample, whereineach set of images of the plurality of sets of images are capturedsimultaneously, wherein each camera sensor of the array of camerasensors captures one image for each set of images of the plurality ofsets of images; and create a plurality of 3D tomographic reconstructionimages from the plurality of sets of images; wherein an image of theplurality of 3D tomographic reconstruction images is created for eachset of images of the plurality of sets of images.